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llsignedxor

int.llsignedxor

fn llsignedxor(r: []Limb, a: []const Limb, a_positive: bool, b: []const Limb, b_positive: bool) bool

File

lib/std/math/big/int.zig:4447

Code

fn llsignedxor(r: []Limb, a: []const Limb, a_positive: bool, b: []const Limb, b_positive: bool) bool {
    assert(a.len != 0 and b.len != 0);
    assert(r.len >= a.len);
    assert(a.len >= b.len);

    // If a and b are positive, the result is positive and r = a ^ b.
    // If a negative, b positive, result is negative and we have
    // r = --(--a ^ b)
    //   = --(~(-a - 1) ^ b)
    //   = -(~(~(-a - 1) ^ b) + 1)
    //   = -(((-a - 1) ^ b) + 1)
    // Same if a is positive and b is negative, sides switched.
    // If both a and b are negative, the result is positive and we have
    // r = (--a) ^ (--b)
    //   = ~(-a - 1) ^ ~(-b - 1)
    //   = (-a - 1) ^ (-b - 1)
    // These operations can be made more generic as follows:
    // - If a is negative, subtract 1 from |a| before the xor.
    // - If b is negative, subtract 1 from |b| before the xor.
    // - if the result is supposed to be negative, add 1.

    var i: usize = 0;
    var a_borrow = @intFromBool(!a_positive);
    var b_borrow = @intFromBool(!b_positive);
    var r_carry = @intFromBool(a_positive != b_positive);

    while (i < b.len) : (i += 1) {
        const ov1 = @subWithOverflow(a[i], a_borrow);
        a_borrow = ov1[1];
        const ov2 = @subWithOverflow(b[i], b_borrow);
        b_borrow = ov2[1];
        const ov3 = @addWithOverflow(ov1[0] ^ ov2[0], r_carry);
        r[i] = ov3[0];
        r_carry = ov3[1];
    }

    while (i < a.len) : (i += 1) {
        const ov1 = @subWithOverflow(a[i], a_borrow);
        a_borrow = ov1[1];
        const ov2 = @addWithOverflow(ov1[0], r_carry);
        r[i] = ov2[0];
        r_carry = ov2[1];
    }

    // If both inputs don't share the same sign, an extra limb is required.
    if (a_positive != b_positive) {
        r[i] = r_carry;
    } else {
        assert(r_carry == 0);
    }

    assert(a_borrow == 0);
    assert(b_borrow == 0);

    return a_positive == b_positive;
}